This is a survey of M-regularity and its applications, expanding on lectures given by the second author at the Seattle conference, in August 2005, and at the Luminy workshop " Géométrie Algébrique Complexe " , in October 2005 1 .

Nous montrons la densité des cycles répulsifs dans l’ensemble de Julia des fonctions méromorphes transcendantes à une variable complexe, sans utiliser le théorème des cinq ı̂les d’Ahlfors ni la théorie de Nevanlinna.

This is a survey of M -regularity and its applications, expanding on lectures given by the second author at the Seattle conference, in August 2005, and at the Luminy workshop ”Géométrie Algébrique Complexe”, in October 2005.